You can access the Lab's Github Repository by clicking the link below

Lab Projects

1. MAGIC (Markov Affinity-based Graph Imputation of Cells): an algorithm that uses graph signal processing for denoising and missing transcript recovery in single cell RNA sequencing. MAGIC successfully recovers gene-gene relationships from data and allows for the prediction of transcription targets.

2. PHATE (Potential of Heat-diffusion Affinity-based Transition Embedding): a visualization and dimensionality reduction technique that is sensitive to local and global relationships and successfully preserves structures of interest in biological data including cluster structure and branching trajectory structure.

3. SAUCIE (Sparse AutoEncoders for Clustering Imputation and Embedding): a deep autoencoder architecture that allows for unsupervised exploration of data, and has novel regularizations that allow for data denoising, batch normalization, clustering and visualization simultaneously  in various layers of the network.

4. DREMI (conditional Density-based Resampled Estimate of Mutual Information): a computational method based on established statistical concepts, to characterize signaling network relationships by quantifying the strengths of network edges and deriving signaling response functions.

4. MELD (Manifold Enhancement of Latent Dimensions): a graph signal processing tool to analyze multiple scRNA-seq samples from two or more conditions.

5. PhEMD (Phenotypic Earth Mover’s Distance): a computational method to quantify relationships between drug perturbations on dozens to hundreds of single cell samples.

6. DREMI (conditional Density-based Resampled Estimate of Mutual Information): a computational method based on established statistical concepts, to characterize signaling network relationships by quantifying the strengths of network edges and deriving signaling response functions.

7. DyMoN (Dynamics Modeling Networks): A neural network framework for learning stochastic dynamics for generative and embedding purposes. DyMoN serves as a deep model that itself embodies a dynamic system such that the gene logic and features driving the system can be studied.

8. SUGAR (Synthesis Using Geometrically Aligned Random-walks): A new kind of data generation algorithm that generates of data geometry rather than density and is able to generate data in sparse regions and predicts hypothetical data points.

9. MAGAN (Manifold Alignment Generative Adversarial Network): a  dual GAN (generative adversarial network) framework that can find correspondences between two data modalities measuring the same system to create an integrated dataset.

10. Neuron Editing: a neural network inference method which maps between datasets with the signal learned on a subset of the data, for example when a drug perturbation is applied to one cell type neuron editing can be used to apply it in silico to another cell type.

MAGIC: Recovering Gene Interactions from
Single-Cell Data Using Data Diffusion

David van Dijk, Roshan Sharma, Juozas Nainys, Kristina Yim, Pooja Kathail, Ambrose J. Carr, Cassandra Burdziak, Kevin R. Moon, Christine L. Chaffer, Diwakar Pattabiraman, Brian Bierie, Linas Mazutis, Guy Wolf, Smita Krishnaswamy, Dana Pe’er

You can access MAGIC's Github repository and article page by clicking the links below


Single-cell RNA-sequencing is fast becoming a major technology that is revolutionizing biological discovery in fields such as development, immunology and cancer. The ability to simultaneously measure thousands of genes at single cell resolution allows, among other prospects, for the possibility of learning gene regulatory networks at large scales. However, scRNA-seq technologies suffer from many sources of significant technical noise, the most prominent of which is dropout due to inefficient mRNA capture. This results in data that has a high degree of sparsity, with typically only 10% non-zero values.

To address this, we developed MAGIC (Markov Affinity-based Graph Imputation of Cells), a method for imputing missing values, and restoring the structure of the data. After MAGIC, we find that two- and three-dimensional gene interactions are restored and that MAGIC is able to impute complex and non-linear shapes of interactions. MAGIC also retains cluster structure, enhances cluster-specific gene interactions and restores trajectories, as demonstrated in mouse retinal bipolar cells, hematopoiesis, and our newly generated epithelial-to-mesenchymal transition dataset.



PHATE: Visualizing Transitions and Structure for
Biological Data Exploration

Kevin R. Moon, David van Dijk, Zheng Wang, Daniel Burkhardt, William Chen, Antonia van den Elzen, Matthew J Hirn, Ronald R Coifman, Natalia B Ivanova, Guy Wolf, Smita Krishnaswamy*

You can access PHATE's Github repository and bioRxiv preprint by clicking the links below


In the era of 'Big Data' there is a pressing need for tools that provide human interpretable visualizations of emergent patterns in high-throughput high-dimensional data. Further, to enable insightful data exploration, such visualizations should faithfully capture and emphasize emergent structures and patterns without enforcing prior assumptions on the shape or form of the data.

In this paper, we present PHATE (Potential of Heat-diffusion for Affinity-based Transition Embedding) - an unsupervised low-dimensional embedding for visualization of data that is aimed at solving these issues. Unlike previous methods that are commonly used for visualization, such as PCA and tSNE, PHATE is able to capture and highlight both local and global structure in the data. 


SAUCIE: Exploring Single-Cell Data with
Deep Multitasking Neural Networks

Matthew Amodio, Krishnan Srinivasan, David van Dijk, Hussein Mohsen, Kristina Yim, Rebecca Muhle, Kevin R Moon, Susan Kaech, Ryan Sowell, Ruth Montgomery, James Noonan, Guy Wolf, Smita Krishnaswamy

You can access SAUCIE's Github repository and bioRxiv preprint by clicking the links below


Handling the vast amounts of single-cell RNA-sequencing and CyTOF data, which are now being generated in patient cohorts, presents a computational challenge due to the noise, complexity, sparsity and batch effects present. Here, we propose a unified deep neural network-based approach to automatically process and extract structure from these massive datasets.

Our unsupervised architecture, called SAUCIE (Sparse Autoencoder for Unsupervised Clustering, Imputation, and Embedding), simultaneously performs several key tasks for single-cell data analysis including 1) clustering, 2) batch correction, 3) visualization, and 4) denoising/imputation. SAUCIE is trained to recreate its own input after reducing its dimensionality in a 2-D embedding layer which can be used to visualize the data.

Additionally, SAUCIE uses two novel regularizations: (1) an information dimension regularization to penalize entropy as computed on normalized activation values of the layer, and thereby encourage binary-like encodings that are amenable to clustering and (2) a Maximal Mean Discrepancy penalty to correct batch effects. Thus SAUCIE has a single architecture that denoises, batch-corrects, visualizes and clusters data using a unified representation. We show results on artificial data where ground truth is known, as well as mass cytometry data from dengue patients, and single-cell RNA-sequencing data from embryonic mouse brain.



 MELD - Graph signal processing identifies cell populations affected by an experimental treatment

View our preprint on BioRxiv

Single-cell RNA-sequencing (scRNA-seq) is a powerful tool to quantify transcriptional states in thousands to millions of cells. It is increasingly common for scRNA-seq data to be collected in multiple experimental conditions, yet quantifying differences between scRNA-seq datasets remains an analytical challenge. Previous efforts at quantifying such differences focus on discrete regions of the transcriptional state space such as clusters of cells. Here, we describe a continuous measure of the effect of an experiment across the transcriptomic space. First, we use the manifold assumption to model the cellular state space as a graph with cells as nodes and edges connecting cells with similar transcriptomic profiles. Next, we create an Enhanced Experimental Signal (EES) that estimates the likelihood of observing cells from each condition at every point in the manifold. We show that the EES has useful properties and information. First, it allows us to identify how gene expression is affected by a given perturbation, including identifying non-monotonic changes from only two conditions. Second, we show that we can use both the magnitude and frequency of the EES, using an algorithm we call vertex frequency clustering, to derive subsets of cells at appropriate levels of granularity that are enriched in the experimental or control conditions or that are unaffected between conditions. We demonstrate both algorithms using a combination of biological and synthetic datasets.

PhEMD - comparing drug perturbations by their effect on single cell populations

William S. Chen, Nevena Zivanovic, David van Dijk, Guy Wolf, Bernd Bodenmiller, Smita Krishnaswamy

You can access the arXiv preprint by clicking the link below

Previously, the effect of a drug on a cell population was measured based on simple metrics such as cell viability. However, as single-cell technologies are becoming more advanced, drug screen experiments can now be conducted with more complex readouts such as gene expression profiles of individual cells. The increasing complexity of measurements from these multi-sample experiments calls for more sophisticated analytical approaches than are currently available.

We develop a novel method called PhEMD (Phenotypic Earth Mover's Distance) and show that it can be used to embed the space of drug perturbations on the basis of the drugs' effects on cell populations. When testing PhEMD on a newly-generated, 300-sample CyTOF kinase inhibition screen experiment, we find that the state space of the perturbation conditions is surprisingly low-dimensional and that the network of drugs demonstrates manifold structure.

We show that because of the fairly simple manifold geometry of the 300 samples, we can accurately capture the full range of drug effects using a dictionary of only 30 experimental conditions. We also show that new drugs can be added to our PhEMD embedding using similarities inferred from other characterizations of drugs using a technique called Nystrom extension.

Our findings suggest that large-scale drug screens can be conducted by measuring only a small fraction of the drugs using the most expensive high-throughput single-cell technologies -- the effects of other drugs may be inferred by mapping and extending the perturbation space. We additionally show that PhEMD can be useful for analyzing other types of single-cell samples, such as patient tumor biopsies, by mapping the patient state space in a similar way as the drug state space.

We demonstrate that PhEMD is highly scalable, compatible with leading batch effect correction techniques, and generalizable to multiple experimental designs. Altogether, our analyses suggest that PhEMD may facilitate drug discovery efforts and help uncover the network geometry of a collection of single-cell samples.


DREMI: Conditional Density-based Analysis
of T cell Signaling in Single Cell Data

Smita Krishnaswamy, Matthew H. Spitzer, Michael Mingueneau, Sean C Bendall, Oren Litvin, Erica Stone, Dana Pe’er* and Garry P Nolan

Dremi is currently part of the Krishnaswamy Lab scprep stats toolkit. Click the following links to find the code on Github or read the article in Science.


Cellular circuits sense the environment, process signals, and compute decisions using networks of interacting proteins. To model such a system, the abundance of each activated protein species can be described as a stochastic function of the abundance of other proteins. High-dimensional single-cell technologies, like mass cytometry, offer an opportunity to characterize signaling circuit-wide. However, the challenge of developing and applying computational approaches to interpret such complex data remains.

Here, we developed computational methods, based on established statistical concepts, to characterize signaling network relationships by quantifying the strengths of network edges and deriving signaling response functions. In comparing signaling between naïve and antigen-exposed CD4+ T-lymphocytes, we find that although these two cell subtypes had similarly-wired networks, naïve cells transmitted more information along a key signaling cascade than did antigen-exposed cells.

We validated our characterization on mice lacking the extracellular-regulated MAP kinase (ERK2), which showed stronger influence of pERK on pS6 (phosphorylated-ribosomal protein S6), in naïve cells compared to antigen-exposed cells, as predicted. We demonstrate that by using cell-to-cell variation inherent in single cell data, we can algorithmically derive response functions underlying molecular circuits and drive the understanding of how cells process signals.



TIDES: Learning time-varying information flow from
single-cell epithelial to mesenchymal transition data

Smita Krishnaswamy, Nevena Zivanovic, Roshan Sharma, Dana Pe’er, Bernd Bodenmiller

You can access the publication in PLOS ONE by following the link below


TIDES or ( Trajectory Interpolated DREMI Scores) is an extension of our earlier Density Resampled Estimate of Mutual Information which quantifies time-varying edge behavior over a developmental trajectory. In particular it tracks times during development in which a regulatory relationship is strong (high mutual information) vs times when regulatory relationships are inactive (low mutual information) due to regulatory network rewiring that underlies differentiation. We also predict an overall metric of edge dynamism, which combined with TIDES allows us to predict the effect of drug perturbations on the Epithelial-to-Mesenchymal transition in breast cancer cells.


Dynamics Modeling Networks:
Modeling Dynamics of Biological Systems with
Deep Generative Neural Networks

David van Dijk*, Scott Gigante*, Kevin Moon, Alexander Strzalkowski, Katie Ferguson, Jess Cardin, Guy Wolf, Smita Krishnaswamy

You can access the arXiv preprint by clicking the link below


Biological data often contains measurements of dynamic entities such as cells or organisms in various states of progression. However, biological systems are notoriously difficult to describe analytically due to their many interacting components, and in many cases, the technical challenge of taking longitudinal measurements.

This leads to difficulties in studying the features of the dynamics, for examples the drivers of the transition. To address this problem, we present a deep neural network framework we call Dynamics Modeling Network or DyMoN. DyMoN is a neural network framework trained as a deep generative Markov model whose next state is a probability distribution based on the current state.

DyMoN is well-suited to the idiosyncrasies of biological data, including noise, sparsity, and the lack of longitudinal measurements in many types of systems. Thus, DyMoN can be trained using probability distributions derived from the data in any way, such as trajectories derived via dimensionality reduction methods, and does not require longitudinal measurements.

We show the advantage of learning deep models over shallow models such as Kalman filters and hidden Markov models that do not learn representations of the data, both in terms of learning embeddings of the data and also in terms training efficiency, accuracy and ability to multitask. We perform three case studies of applying DyMoN to different types of biological systems and extracting features of the dynamics in each case by examining the learned model.


SUGAR: Geometry-Based Data Generation

Ofir Lindenbaum, Jay S. Stanley III, Guy Wolf, Smita Krishnaswamy

You can access the arXiv preprint and NeurIPS poster by clicking the links below


Many generative models attempt to replicate the density of their input data. However, this approach is often undesirable, since data density is highly affected by sampling biases, noise, and artifacts. We propose a method called SUGAR (Synthesis Using Geometrically Aligned Random-walks) that uses a diffusion process to learn a manifold geometry from the data. Then, it generates new points evenly along the manifold by pulling randomly generated points into its intrinsic structure using a diffusion kernel.

SUGAR equalizes the density along the manifold by selectively generating points in sparse areas of the manifold. We demonstrate how the approach corrects sampling biases and artifacts, while also revealing intrinsic patterns (e.g. progression) and relations in the data. The method is applicable for correcting missing data, finding hypothetical data points, and learning relationships between data features.

MAGAN: Aligning Biological Manifolds

Matthew Amodio and Smita Krishnaswamy

You can access the PMLR publication by clicking the link below

It is increasingly common in many types of natural and physical systems (especially biological systems) to have different types of measurements performed on the same underlying system. In such settings, it is important to align the manifolds arising from each measurement in order to integrate such data and gain an improved picture of the system; we tackle this problem using generative adversarial networks (GANs). Recent attempts to use GANs to find correspondences between sets of samples do not explicitly perform proper alignment of manifolds.

We present the new Manifold Aligning GAN (MAGAN) that aligns two manifolds such that related points in each measurement space are aligned. We demonstrate applications of MAGAN in single-cell biology in integrating two different measurement types together: cells from the same tissue are measured with both genomic (single-cell RNA-sequencing) and proteomic (mass cytometry) technologies. We show that MAGAN successfully aligns manifolds such that known correlations between measured markers are improved compared to other recently proposed models.


Out-of-Sample Extrapolation with Neuron Editing

Matthew Amodio, David van Dijk, Ruth Montgomery, Guy Wolf, Smita Krishnaswamy

You can access the arXiv preprint by clicking the link below

While neural networks can be trained to map from one specific dataset to another, they usually do not learn a generalized transformation that can extrapolate accurately outside the space of training. For instance, a generative adversarial network (GAN) exclusively trained to transform images of cars from light to dark might not have the same effect on images of horses. This is because neural networks are good at generation within the manifold of the data that they are trained on. However, generating new samples outside of the manifold or extrapolating "out-of-sample" is a much harder problem that has been less well studied.

To address this, we introduce a technique called neuron editing that learns how neurons encode an edit for a particular transformation in a latent space. We use an autoencoder to decompose the variation within the dataset into activations of different neurons and generate transformed data by defining an editing transformation on those neurons.

By performing the transformation in a latent trained space, we encode fairly complex and non-linear transformations to the data with much simpler distribution shifts to the neuron's activations. We showcase our technique on image domain/style transfer and two biological applications: removal of batch artifacts representing unwanted noise and modeling the effect of drug treatments to predict synergy between drugs.